The generic value set of a two-generator semigroup

We give a simple recursion for the minimal generators $G=\{g_i\}$ of the generic value set ${\mathrm{\Lambda }}_{gen}$ of a plane curve germ $C$ with a two-generator semigroup $\mathrm{\Gamma }⟨p,m⟩$. The main result provides for explicit calculation of all $g_i$ and shows that they are in fact minimal generators. Explicit formulas for the cardinality of the minimal generators $\mathrm{\mid }G\mathrm{\mid }$ and for the conductor $c({\mathrm{\Lambda }}_{gen})$ of ${\mathrm{\Lambda }}_{gen}$ are given. The recursion can be used to compute the generic Tjurina number ${\tau }_{gen}$ in this case, a method we compare to that given by Alberich-Carramiñana, Almirón, Blanco, and Melle-Hernández (arXiv:1904.02652). The main result is based on the non-explicit algorithm and ideas of Delorme.